Math 300: Mathematical Computing

Matlab ICE

Recall that we can approximate the derivative of a function f
at a point x using the formula

f'(x) ~ Fh = (f(x+h)-f(x-h)) / (2h).

For this exercise, you must write a function deriv_test that takes three
arguments: the function f, the point where the derivative is to be approximated x, and the correct value of the derivative. Thus, the
function will be called as deriv_test(f,x,correct).
The function will compute the above approximation to the derivative
for values of h going down in powers of ten, with exponent p,
from 10-1
to 10-16. It will plot the absolute error
|f'(x)-Fh| for each of those values of p = -1, -2, ..., -16.
In other words, the power p of 10 is on the horizontal axis,
and the error is on the vertical axis.
The function must return the vector of approximations to the
derivative.